Question

do males or females feel more tense or stressed out at work? a survey of employed adults conducted online by a company on behalf of a research organization revealed the data in the contingency table shown to the right. complete parts (a) through (d) below.

	gender
yes	305	315	620
no	200	100	300
total	505	415	920

a. what is the probability that a randomly selected person’s gender is female? 0.451 (type an integer or a decimal. round to three decimal places as needed.)
b. what is the probability that a randomly selected person feels tense or stressed out at work and is female? 0.342 (type an integer or a decimal. round to three decimal places as needed.)
c. what is the probability that a randomly selected person feels tense or stressed out at work or is female? (type an integer or a decimal. round to three decimal places as needed.)

Explanation:

Part (a)

Step1: Find total number of people

Total number of people is the sum of all totals, which is \(505 + 415 = 920\) (or from the "Total" row, it's 920).

Step2: Find number of females

Number of females is 415 (from the "Female" column total).

Step3: Calculate probability

Probability \(P(\text{Female})=\frac{\text{Number of Females}}{\text{Total Number of People}}=\frac{415}{920}\approx0.451\)

Step1: Find number of females who felt tense or stressed

From the table, females who felt tense or stressed (Yes) is 315.

Step2: Total number of people is 920.

Step3: Calculate probability

Probability \(P(\text{Yes and Female})=\frac{\text{Number of Females who said Yes}}{\text{Total Number of People}}=\frac{315}{920}\approx0.342\)

Step1: Use the formula for probability of union: \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Let \(A\) be "feels tense or stressed" and \(B\) be "female".

Step2: Find \(P(A)\), \(P(B)\), \(P(A\cap B)\)

• \(P(A)=\frac{620}{920}\) (number of people who said Yes is 620)
• \(P(B)=\frac{415}{920}\) (number of females is 415)
• \(P(A\cap B)=\frac{315}{920}\) (number of females who said Yes is 315)

Step3: Calculate \(P(A\cup B)\)

\(P(A\cup B)=\frac{620 + 415 - 315}{920}=\frac{720}{920}\approx0.783\)

Answer:

\(0.451\)

Part (b)